Tunable interactions in ultracoldgases have led to important breakthroughs in atomic physics over the past decade, including the realization of strongly interacting Fermi [ O’H02; KZ08; Blo08 ] to the observation of Efimov trimers [ Kra06 ] . Typically, interactions are tuned using a magnetic Feshbach resonance, where an external magnetic field tunes the energy of a colliding atom pair to be degenerate with a molecular bound state. However, mag- netic tuning of interactions lacks high-resolution spatial control, due to the size of the magnetic coils used in ultracold experiments. Also, magnetic tuning cannot achieve fast temporal control due to the high-inductance of the coils. Optical control of interactions can achieve high-resolution in both space and time, but generally suffers from atom loss due to spontaneous scattering.
Just as we worked to establish a set of plausible initial data for the wavefunction of a solid classical body that was consistent with the usual phonon and solid state electron orbital cal- culations, we would like to give some plausible subclass of wavefunctions that correspond to a gas that is thermalized and hydrodynamic. In the case of the Gross-Pitaevskii equation for a condensed bosonic gas, we often consider the order to parameter to be a scaled copy of a single particle wavefunction and all the particles to be “in the same state” as in Sec. 5.3. This is a manifestly single body descriptions of the situation. It is not manifestly clear this makes sense. After all, the “g” that describes the interaction strength (usually in terms of the scattering length) typically is a subtle combination of both potential energy of the interactions and ki- netic energy of the wavefunction oscillations about the two-body diagonals so not the same “g” that governs the strength of the contact potential. One can derive a static version of the GP equation from the result of LHY  or Bogoliubov  theory by applying mean field theory. Extensions of this to time dependence, especially with higher order corrections, as in the case of Bogoliubov-Hartree-Fock theory, introduce unphysical gaps in the energy spectrum or violate conservation laws . Despite these efforts, experiment seems to show that the case of very low T bosonic systems are very correlated systems, rigid enough that they only require a single order parameter for their description. Persistent vortices can occur and hence these gases are often dubbed superfluid, often leading to the inference that the two fluid model is applicable. It is certainly true that any bosonic or fermionic cloud at arbitrarily large internal energy, can possess internal vorticity. The distinction is that these will not generally give depressions in the one-body density function ρ(x) and that the angular momentum may not be N ~ .
Binary collisions in such confined systems are usually studied in the context of s-wave scattering by means of a very simple model, where the atoms are con- fined in two of the spatial directions by means of harmonic    or infi- nite quantum well   potentials and the interaction between two colliding atoms is modeled by the regularized Huang’s pseudopotential . The strength of the Huang’s potential corresponds to the theoretical representation of the tunable interaction between the atoms by Feshbach resonance    in actual experiments. In these approaches, the scattering amplitude is determined by means of the expansion of the scattering wave function    into the eigenstates of the transverse unperturbed (Huang’s potential independent) Ha- miltonian. As a result, it is possible to relate the effective 1D coupling strength to the s-wave scattering length (an experimentally accessible quantity, related to the Feshbach resonance interaction), showing the existence of phenomena such as CIRs  - and multiple CIRs       and provid- ing the connection between theoretical and experimental quantities in the study of ultracoldgases.
The problem of dissipationless spin transport is a widely studied topic in condensed matter physics with important applications to electron-hole su- perfluidity, superfluid 3 He and spintronic devices . Ultracoldgases, with the possibility they offer to realize quantum degenerate mixtures, open new interesting perspectives for the investigation of spin dynamics. Spin diffusion in a strongly interacting two-component Fermi gas has been observed and characterized in a series of recent experiments [101, 102, 103], whereas the existence of spin supercurrents in Bose mixtures has been demonstrated both at very low temperatures [104, 105, 106, 107, 108, 109] and in the presence of a large thermal component . In this respect one-dimensional (1D) mixtures are particularly interesting for several reasons: i) the low-energy dynamics is universal and described by the Luttinger liquid model ; ii) spin and charge degrees of freedom are expected to be completely decoupled at low energy [112, 113]; and, finally, iii) regimes of strong interactions can be achieved in long-lived samples [73, 80, 75, 76]. The undamped propa- gation of spin waves is an important signature of spin superfluidity and an unbiased determination of the spin-sound velocity is a crucial element to understand the dynamics of two-component Bose mixtures at ultralow tem- peratures. Notably, for such mixtures, the propagation of sound in the spin channel depends not only on the static magnetic susceptibility, but also on a purely dynamic quantity known as the Andreev-Bashkin non-dissipative drag . This intriguing effect, never observed so far, involves two cou- pled superfluids and entails that a superflow in one component can induce
Even if the effective hamiltonian of ultracoldgases can be simple, due to the diluteness of the system and the low temperature, which imply low energy physics, the solution of the quantum mechanic equations governing the state of these systems is not always simple. For the static properties usually mean-field solutions exist or perturbative expansions can be pro- duced in some regimes. However Quantum Monte Carlo (QMC) techniques provide more accurate results especially in the strongly interacting regimes. For confined systems it is possible to use QMC only for a few particles, so that, for large number of particles, a fruitful combined use of Density Func- tional Theory (DFT) and QMC is necessary. The study of the dynamics of ultracoldgases has received little attention with QMC techniques, due to the intrinsic computational difficulty of the many-body problem, so that general hydrodynamic equations are often used for studying the propagation of smoothly varying perturbations.
While these ion-production channels lead to atom loss and therefore degrade the per- formance of the MOT, their most detrimental effect is on the trapped ions. Because these ions are produced at random locations in the trap, they can lead to large heat loads on the ions and, in some cases, loss of the desired molecular ions from the trap. We have found that this effect can be mitigated, in Ca at least, by operating the ion trap in a regime where Ca + and/or Ca + 2 are not stable – note this may not always be possible since the requisite stability of the desired molecular ion may preclude it. In this regime, the ions are created and then immediately ejected from the trap with minimal effect on the trapped ions. The Smith group at UCONN has also implemented secular frequency excitation to remove unwanted Na + 2 ions, produced through PAI, from their experiments . It may also be possible to use an intercombination MOT, in e.g. Sr, to produce an ultracold alka- line earth-gas without producing ions, though the reactivity of these long-lived excited states may become problematic.
Abstract. We demonstrate efficient transfer of ultracold molecules into a deeply bound rovibrational level of the singlet ground state potential in the presence of an optical lattice. The overall molecule creation efficiency is 25%, and the transfer efficiency to the rovibrational level |v = 73 , J = 2 i is above 80%. We find that the molecules in |v = 73 , J = 2 i are trapped in the optical lattice, and that the lifetime in the lattice is limited by optical excitation by the lattice light. The molecule trapping time for a lattice depth of 15 atomic recoil energies is about 20 ms. We determine the trapping frequency by the lattice phase and amplitude modulation technique. It will now be possible to transfer the molecules to the rovibrational ground state |v = 0 , J = 0 i in the presence of the optical lattice.
Magnetic ring-shaped traps have been proposed and realised using either static [28, 29, 30] or time-averaged [31, 32, 33] magnetic fields. In purely magnetic traps, to reduce the size of the system, the current-carrying wires – needed to connect the system to an external electric source – get closer to the trap region, perturbing the rotational symmetry of the potential. Furthermore, fragmentation of atomic clouds has been seen for magnetically trapped gases lying close to current carrying wires in atom chips [34, 35, 36, 37, 38]. This was attributed to corrugations or irregular domain structure in the conductor that deflect the current from the desired path. A way to circumvent this is the use of alternating current to ‘time-average’ away the defects . The need to obtain an ultra-smooth ring trap, with no end effects due to input/output wires and the inherent magnetic smoothness of an ac current, led to the proposal of a time-averaged toroidal trap based on a conducting ring driven by magnetic induction . This trap has now been experimentally realised , however although the trap works well at ring radii of a few mm, it is not scalable down into the sub-mm regime required for atom chips. This is because time-orbiting potential (TOP) traps [31, 39] require ω T ≪ ω TOP ≪ ω L where the subscripts T, TOP and L
In summary, we show that complex one-dimensional guides for ultracold matter can be deﬁned by inductive effects over metallic and superconducting loops. A very ﬂexible wave-guide shape is possible as the guide simply follows the curves of a metal track laid down as a loop on the surface of an atom-chip or carved into it. For operation, the loop should receive a magnetic ﬁeld that oscillates near to resonance with the hyperﬁne splitting of the atomic ground state of the atoms. The ﬁeld induces an electric current on the conducting track without the need of leading wires that might introduce undesired asymmetries in the potential landscape. The combined applied and induced ﬁelds form a trapping structure for the atoms.
Photoassociation (PA) of ultracold atoms, in which two interacting ultracold atoms are resonantly excited by a laser to bound states of the associated molecule, is a widely used technique to study the dynamics of ultracold collisions in dilute quantum gases. Of particular interest is PA in meta- stable rare gases where novel experimental strategies based upon their large internal energy can be implemented.
Slow light refers to light whose velocity is on the order of metres per second or even less . Clearly, to obtain such a fantastic reduction in phase velocity, one would need a correspondingly large refractive index, which is not simple to achieve. We turn instead to a quantum mechanical trick which causes light to take a very long time to traverse a given distance through its constant absorption and reemission by atoms of the material. A pulse of light can be considered as the point at which the various frequency components which comprise it are in phase. Using this trick, these frequency components are dispersed, causing the place where they are in phase to eectively be shifted back, hence slowing the beam; it is the group velocity of the light pulse which is slowed as opposed to the phase velocity. This method is known as Electromagnetically Induced Transparency (EIT) ; it is frequently used in dilute alkali vapours and has also been used in Bose-Einstein condensates ; as we have seen, it also has the potential for the creation of black hole analogues. Ultracold atoms , with their relatively small vibrational motion, allow properties where slow light interaction leads to motion, such as the Iordanskii force, to be investigated with greater ease; we will discuss such eects in greater detail in a later chapter.
of a BEC below a certain critical velocity (c.f. no disturbance to the flow of the su- perfluid by an obstacle) ; demonstrations of vortex arrays (signifying irrotational flow) [19, 20, 21]; and persistent flow of a rotating toroidal BEC [22, 23]. These cold atomic and molecular systems are seen as a step forward in studying superfluidity (and the related field of superconductivity), as other interactions common to con- densed matter systems, e.g. van der Waals interactions in liquid helium, are much reduced. This, added to the high degree of control over atoms available due to their sensitivity to electric and magnetic fields, means they are an ideal system for studying superfluidity in the hope of gaining greater insight into the phenomenon. In particular, quantum degenerate Fermi gases with their Cooper pairs bear a close resemblance to superconductors, and have raised hopes for an explanation for high temperature superconductivity.
Some meth ods to deter mine the overpressure/impulse require an esti mate of the flam ma ble mass. Esti ma tion of the total flam ma ble mass within the vapor cloud is dif fi cult. A detailed mono graph on this com plex sub ject is pro vided else - where (AIChE, 1999b). Ide ally, a dis per sion model could be used to deter mine the flam ma ble mass in the vapor cloud that is between the upper and lower flammability limits. Dis per sion mod el ing of flam ma ble gases is com plex and the models have not been val i dated for con gested vol umes. At flam ma ble con cen tra - tions the cloud is typ i cally dense. The dense gas prob lem is three dimen sional, requir ing numer i cal or ana lyt i cal inte gra tion of the con cen tra tion pro files within the cloud. It is also not clear what con cen tra tion to use for the extent of cloud com - bus tion. The dis per sion models do not account for vari a tions in instan ta neous cloud con cen tra tions which may result in non uni form burn ing of the vapor cloud. Fur ther more, there is some evi dence that a fuel–air mix ture will burn beyond the flammability limits by overdriving it with an ener getic igni tion source. As a result of these dif fi cul ties, some risk ana lysts use a con ser va tive con cen tra tion limit to define the com bus ti ble cloud equal to one-half of the lower flammability limit (AIChE, 1999a, 2000). Dis per sion mod el ing is discussed further in several CCPS books (AIChE, 1996a; Hanna and Britter, 2002).
The Zak phase plays an important role in the modern understanding of the macro- scopic polarization in crystalline dielectrics [7, 21, 22, 124]. The polarization is given by the electric dipole moment per volume. In crystals, it cannot be defined uniquely due to the periodicity of the charge density, but its value depends on the choice of origin . In spite of its very basic character and great relevance, a complete theory of polarization was developed only in the 1990s [21, 22]. This theory focuses on the change in polar- ization between two configurations as opposed to its absolute value because the latter has no physical significance. This approach is closely related to charge pumping since the polarization difference is given by the charge transport during an adiabatic evolution con- necting the two states in question. Accordingly, the rate of change in the polarization is proportional to the anomalous velocity. Following the derivation above, the polarization difference between two configurations for dielectric media can be expressed as the differ- ence of the Zak phases similar to Eq. (2.26) . This allows for an efficient computation because only the initial and final states are required. However, due to the periodicity of the potential, the polarization change can only be defined up to a displacement by an in- teger multiple of unit cells since an arbitrary number of closed cycles can be added to the path. While the Zak phase can in principle take any value, it can be shown that in inver- sion symmetric systems it is restricted to multiples of π . Furthermore, while the Zak phase is gauge invariant with respect to the phase choice for the Bloch wave functions, it does depend on the choice of origin – just like the absolute value of the polarization. This position dependence is important in the context of Wannier-Stark ladders, where the Zak phase was first introduced, as it leads to a correction in the energy spectrum that ensures translational invariance [20, 126]. The Zak phase is also of importance for the existence of edge states in 1D systems  as well as excitations with fractional charges [128–130] and has recently been measured with ultracold atoms in a dimerized optical lattice .
We demonstrate the generation of highly adaptable and reproducible dark optical ring lattices, which do not require Laguerre–Gauss beams or interferometric stability. In conjunction with a magnetic trap, these scanned 2D intensity distributions will enable low-decoherence trapping and straightforward dynamic manipulation of ultracold species in annular geometries using low-intensity regions of blue-detuned light. The technique is ideal for azimuthal ratchet, Mott insulator and persistent current experiments with quantum degenerate gases.
The neutron was first discovered in 1932 as a neutral particle with roughly the same mass as the hydrogen atom, but with an unprecedented ability to penetrate deep into matter. First proposed in 1920 by Ernest Rutherford as a component of the nucleus, before its actual discovery, no subatomic particle was known to evade entrapment quite like the neutron. It came as a great surprise then, when Ya. B. Zel’dovich proposed in 1959 [36,37] that neutrons could, in fact, be totally internally trapped by very thin coatings of materials on storage bottle walls, orders of magnitude thinner than the shielding thermal neutrons required to be stopped. The secret sauce was that these neutrons must be ultracold, possessing energies of only a few hundred nanoelectronvolts.